Block equalization method and device with adaptation to the transmission channel

ABSTRACT

Method and device for the equalization of a signal received by a receiver, said signal comprising at least one known data sequence (or probe) and a data block located between a first Probe n-1 and a second probe Probe n. The method comprises a step of estimation of the phase rotation θ of the signal received between the first probe Probe n−1 positioned before the data block to be demodulated and the second probe Probe n positioned after the data block to be demodulated.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a method of equalization and anequalizer suited notably to serial type modems that adapt to thetransmission channel.

[0003] Certain international standardization documents for transmissionmethods such as the STANAG (Standardization NATO Agreement) describewaveforms, to be used for modems (modulators/demodulators), that aredesigned to be transmitted on serial-type narrow channels (3 kHz ingeneral). The symbols are transmitted sequentially at a generallyconstant modulation speed of 2400 bauds.

[0004] Since the transmission channel used (in the HF range of 3 to 30MHz) is particularly disturbed and since its transfer function changesrelatively quickly, all these waveforms have known signals at regularintervals. These signals serve as references and the transfer functionof the channel is deduced from them. Among the different standardizedformats chosen, some relate to high-bit-rate modems, working typicallyat bit rates of 3200 to 9600 bits/s which are sensitive to channelestimation errors.

[0005] To obtain a high bit rate, it is furthermore indispensable to usea complex multiple-state QAM (Quadrature Amplitude Modulation) typemodulation, and limit the proportion of reference signals to thegreatest possible extent so as to maximize the useful bit rate. In otherwords, the communication will comprise relatively large-sized datablocks between which small-sized reference signals will be inserted.

[0006] 2. Description of the Prior Art

[0007]FIG. 1 shows an exemplary structure of a signal described in theSTANAG 4539 in which 256-symbol data blocks alternate with inserted,known 31-symbol blocks (called probes or references), corresponding toabout 11% of the total.

[0008] To assess the impulse response h(t) of the channel at the nthdata blocks, there is a first probe (n−1) positioned before the datablock and a second probe (n) positioned after the data block, enablingan assessment of the transfer function of the channel through thecombined impulse response obtained by the convolution of:

[0009] the impulse response of the transmitter, which is fixed,

[0010] the impulse response of the channel, which is highly variable,

[0011] the impulse response of the receiver, which is fixed, these threeelements coming into play to define the signal received at each point intime.

[0012] To simplify the description, it will be assumed hereinafter thatthis set forms the impulse response of the channel.

[0013] The DFE (Decision Feedback Equalizer) is commonly used in modemscorresponding for example to STANAGs (such as the 4285) where theproportion of reference signals is relatively high and the data blocksare relatively short (for example 32 symbols in the 4285).

[0014] Another prior art method uses an algorithm known as the “BDFE”(Block Decision Feedback Equalizer) algorithm. This method amounts toestimating the impulse response of the channel before and after a datablock and finding the most likely values of symbols sent (data sent)that will minimize the mean square error between the received signal andthe signal estimated from a local impulse response that is assumed to beknown.

[0015] This algorithm, shown in a schematic view with reference to FIG.2, consist especially in executing the following steps:

[0016] a) estimating the impulse response h(t) of the channel having alength of L symbols,

[0017] b) knowing this estimated impulse response,

[0018] c) at the beginning of the data block n comprising N usefulsymbols, eliminating the influence of the symbols of the probe (n−1)placed before (L−1 first symbols),

[0019] d) from the probe (n) placed after the data block, eliminatingthe participation of the symbols of the probe that are disturbed by theinfluence of the last data symbols (L−1 symbols),

[0020] e) from the samples thus obtained, whose number is slightlygreater than the number of data symbols (namely N+L−1), making the bestpossible estimation of the value of the N useful symbols most probablysent.

[0021] The method commonly known and described in the prior arttherefore corresponds, in short, to the following steps:

[0022] estimating the impulse response of the channel before the datablock to be demodulated

[0023] estimating the impulse response of the channel after the datablock eliminating the influence of the known signals (steps c and d),mentioned here above, from the channel

[0024] executing the step e) assuming that the impulse response of thechannel develops regularly (for example linearly) all along the datablock.

[0025] This method performs satisfactorily for little-disturbedtransmission channels that do not vary too rapidly.

[0026] However, once the channel becomes more disturbed and a slightfrequency shift remains in the signal and when no use is made of aweighted decoding algorithm whose drawback is that it requires highcomputation power, the requisite performance level generally is nolonger attained.

[0027] The method according to the invention and the associated BDFE arebased notably on a novel approach which consists especially inestimating a residual total Doppler shift that is valid only for thedata block to be demodulated and in pre-compensating for this shiftbefore implementing a BDFE algorithm or an equivalent known to thoseskilled in the art.

[0028] The description makes use of certain notations adopted, includingthe following:

[0029] e^(n): complex samples sent, spaced out by a symbol and belongingto one of the constellations mentioned further above (known or unknown),

[0030] r^(n): complex samples received, the values of n shall beexplained each time and these samples may possible belong to a probe orto data,

[0031] L: length of the impulse response, in symbols, of the channel tobe estimated,

[0032] P: the number of symbols of a probe,

[0033] N: the number of symbols of a data block,

[0034] a_(−p), . . . a⁻¹: known complex values of the symbols of a probepreceding a data block,

[0035] b₀. . . b_(N−1): unknown complex values of the data symbols,

[0036] C_(N). . . C_(N+p−1): complex values of the symbols of a probefollowing a data block,

[0037] d₀. . . d_(p−1): known complex values of the reference symbols,whatever the probe concerned.

SUMMARY OF THE INVENTION

[0038] The invention relates to a method for the equalization of thesignal received by a receiver, said signal comprising at least one knowndata sequence (or probe) and a data block located between a first probeProbe n−1 and a second probe Probe n comprising at least one step forthe estimation of the phase rotation θ of the signal received betweenthe start of the data block and the end of the data block.

[0039] According to the invention, the method estimates the phaserotation between the first probe Probe n−1 positioned before the datablock to be demodulated and the second probe Probe n positioned afterthe data block to be demodulated.

[0040] The method comprises for example a step in which the impulseresponse of the channel is estimated, firstly, by using the first Proben−1 and, secondly, by using the second Probe n and a step in which thedifference between these two estimated impulse response values isminimized.

[0041] The difference between the estimated values of the impulseresponse of the channel can be expressed for example in the form:$E = {\sum\limits_{i = 0}^{L - 1}{{h_{i}^{(N)} - {^{j\quad \theta}h_{i}^{({- P})}}}}^{2}}$

[0042] and the optimum value of the phase rotation θ is determined asbeing the argument of the sum of the conjugate products, that is:$\theta = {a\quad r\quad {g\left( {\sum\limits_{i = 0}^{L - 1}{h_{i}^{(N)}h_{i}^{{({- P})}*}}} \right)}}$

[0043] The method according to the invention may comprise at least thefollowing steps:

[0044] a) estimating the impulse responses h₀(t) and h₁(t) of the probespositioned on either side of the block of data to be analyzed,

[0045] b) estimating the rotation of the phase, θ,

[0046] c) correcting the phase of the frequency of the signal received,and performing a reverse rotation on the data block and the probes,

[0047] d) again jointly estimating the impulse responses by means of themodified probes,

[0048] e) applying a BDFE type data block equalization algorithmfeedback loop.

[0049] The method is advantageously used for the demodulation of signalsreceived in a BDFE device or any other similar device.

[0050] The invention also relates to a device for equalizing at leastone signal that has traveled through a transmission channel, said signalcomprising at least one data block and several probes located on eitherside of the data block, wherein the device comprises at least one meansreceiving the signals and adapted to determining the phase rotation θ ofthe signal or signals received, between a first Probe (n−1) locatedbefore the data block and a second Probe (n) positioned after the datablock, correcting the phase of the received signal, estimating theresponses by means of the probes thus modified and applying a BDFE typealgorithm.

[0051] The object of the present invention has especially the followingadvantages:

[0052] it can be used to attain the required performance levels,especially in the case of highly disturbed transmission channels withfast variations, while only negligibly increasing the computation powerrequirement;

[0053] as compared with the assumption of linear progression commonlyused in the prior art, it enables the elimination of residues of thepoorly compensated-for total Doppler shift.

BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The present invention will be understood more clearly from thefollowing description of an exemplary embodiment given by way of anillustration that in no way restricts the scope of the invention, andmade with reference to the appended drawings of which:

[0055]FIG. 1 shows a general example of the structure of the data to betransmitted,

[0056]FIG. 2 is a diagram of the BDFE algorithm used in the prior art,

[0057]FIG. 3 shows the steps implemented by the method according to theinvention, and

[0058]FIG. 4 is an exemplary functional diagram of the device accordingto the invention.

[0059] The principle of the invention lies notably in the execution ofthe steps shown diagrammatically for example in FIG. 3. These stepsconsist notably in:

[0060] 1—making an estimation, for a first time, of the impulseresponses of the channel before and after the data block, with the probebefore estimation of h₀(t), (1.1) and the probe after estimation ofh₁(t), (1.2) in figure,

[0061] 2—estimating a mean differential rotation between these twopoints in time, t₀ and t₁ expressing a mean rotation of the signal inthe time interval considered, the goal being to minimize the differencebetween the two initial impulse responses, with an estimation of thecommon phase rotation (2),

[0062] 3—locally correcting the frequency of the signal received, inorder to optimize performance, for example to carry out the phasecorrection of the received signal (3),

[0063] 4—making a new estimation, for example jointly, of the impulseresponses is h₀(t) and h₁(t) computed during the first step in takingaccount of the supposed evolution of the channel from one impulseresponse to the other (4),

[0064] 5—executing the BDFE algorithm or an equivalent algorithm byusing the joint estimations of the impulse responses obtained during thefourth step and the data to be demodulated (5).

[0065] The following example refers to FIG. 3 in the non-restrictivecase of an application to a signal having a structure of the kind showndiagrammatically in FIG. 1.

[0066] In a first stage, the method entails a first estimation, forexample separated from the two impulse responses correspondingrespectively to the two probes (Probe n−1 and Probe n) located on eitherside of the data block (data block n) to be assessed.

[0067] The method seeks the best estimation of the L samples of theimpulse response of the channel, referenced h_(0 . . . L−1),

[0068] the signal sent and known is d₀. . . d_(p−1) (d₀ corresponds toa_(−p)in the probe before and to C_(N) in the probe after) and thereceived signal is r₀. . . r_(p−1),

[0069] h the impulse response of the channel is estimated by minimizing,for 5 example, the total mean square error given by: $\begin{matrix}{E = {\sum\limits_{n = N_{0}}^{N_{1}}{{{\sum\limits_{m = 0}^{L - 1}{d_{n - m}h_{m}}} - r_{n}}}^{2}}} & (1)\end{matrix}$

[0070] So that only the known symbols will come into play (i.e. d₀ tod_(p−1) only), we take N₀=L−1 and N₁=P−1.

[0071] The minimizing of E leads to the L following equations:$\begin{matrix}{{\sum\limits_{n = {L - 1}}^{P - 1}{d_{n - p}^{*}\left( {{\sum\limits_{m = \underset{p = {{0\quad \ldots \quad L} - 1}}{0}}^{L - 1}{d_{n - m}h_{m}}} - r_{n}} \right)}} = 0} & (2)\end{matrix}$

[0072] which can be rewritten in the form (3): $\begin{matrix}{{\sum\limits_{m = 0}^{L - 1}{h_{m}\left( {\sum\limits_{\substack{n = {L - 1} \\ p = {{0\quad \ldots \quad L} - 1}}}^{P - 1}{d_{n - m}d_{n - p}^{*}}} \right)}} = {\sum\limits_{n = {L - 1}}^{P - 1}{r_{n}d_{n - p}^{*}}}} & (3)\end{matrix}$

[0073] or again (4):${\sum\limits_{m = \underset{p = {{0\quad \ldots \quad L} - 1}}{0}}^{L - 1}{A_{p,m}h_{m}}} = {B_{p}\quad {with}}$$A_{p,m} = {{\underset{\begin{matrix}\begin{matrix}{n = {L - 1}} \\{m = {{0\quad \ldots \quad L} - 1}}\end{matrix} \\{p = {{0\quad \ldots \quad L} - 1}}\end{matrix}}{\sum\limits^{P - 1}}{d_{n - m}d_{n - p}^{*}}} + {A_{m,p}^{*}\quad {and}}}$$B_{p} = {\sum\limits_{n = {L - \underset{p = {{0\quad L} - 1}}{1}}}^{P - 1}{r_{n}d_{n - p}^{*}}}$

[0074] Since the matrix A={A_(p,m)} is Hermitian, the solution to theproblem is soon found by using the Cholesky decomposition L-U, wellknown to those skilled in the art, where A=L U and:

[0075] L is a lower triangular matrix having only ones on the diagonal,

[0076] U is a higher triangular matrix where the elements of thediagonal are real.

[0077] In practice the matrices L and U are pre-computed (for example ina read-only memory) since the matrix A is formed out of constant values.

[0078] Formally, it can be written that we should have A h=B or L U h=B,which is resolved by bringing into play an intermediate vector y, byfirst of all resolving L y=B then U h=y.

[0079] Estimation of the Instantaneous Drift or Phase Rotation to beApplied

[0080] The method is based on the idea of using a version of jointestimation that starts by estimating a poorly-compensated-for totalDoppler shift, which may be the case when there is a Doppler ramp.

[0081] This is why the method herein uses a version of joint estimationthat starts by estimating a residual shift of this kind, thenpre-compensating for it and implementing a BDFE type algorithm.

[0082] This compensation consists, for example, in stating that betweenthe first probe Probe n−1 positioned before the data block to bedemodulated and the second probe Probe n positioned after the datablock, there has been a total phase modulation equal to a certain angleθ. This mean total rotation is due either to a residue of apoorly-compensated-for frequency shift or to a mean instantaneous shiftin frequency due to the fact that the impulse response of the channelfluctuates in time.

[0083] The reference h^((−P)) _(0 L−1) is attached to the values of theimpulse response h computed by means of the first probe Probe n−1 whichstarts at the −P ranking sample, and the reference h^((N)) _(0 L−1) isattached to the values of the impulse response h computed by means ofthe second probe Probe n which starts at the +N ranking sample.

[0084] The mean rotation θ between these two impulse responses iscomputed by seeking to minimize the difference between the two initialextreme impulse responses computed individually. The effect of this willbe to make the assumption of variation of the responses “more true” (forexample linear), the ideal situation corresponding to the case wherethese two responses become equal.

[0085] More explicitly, this difference has an energy value equal to:$\begin{matrix}{E = {\sum\limits_{i = 0}^{L - 1}{{h_{i}^{(N)} - {^{j\quad \theta}h_{i}^{({- P})}}}}^{2}}} & (5) \\{E = {{cste} - {2\quad {{Re}\left( {^{{- j}\quad \theta}{\sum\limits_{i = 0}^{L - 1}{h_{i}^{(N)}h_{i}^{{({- P})}*}}}} \right)}}}} & (6)\end{matrix}$

[0086] The optimum value of the phase rotation θ is determined as beingthe argument of the sum of the conjugate products, namely:$\begin{matrix}{\theta = {\arg \left( {\sum\limits_{i = 0}^{L - 1}{h_{i}^{(N)}h_{i}^{{({- P})}*}}} \right)}} & (7)\end{matrix}$

[0087] This optimum value corresponds to the total mean rotation thatmust be corrected before executing the steps of an equalizationalgorithm, such as a BDFE algorithm.

[0088] Local Correction of the Frequency of the Signal Received

[0089] Once the value of the mean rotation θ corresponding to theoptimum value mentioned here above has been estimated, the methodcomprises a step in which the original signal samples received r_(n) arereplaced by their values corrected by this local “Doppler” value. Thisis done for the preceding probe, Probe n−1, the data and the probeafter, Probe n, namely for n ranging from −P to P+N−1: $\begin{matrix}\left. r_{n}\rightarrow{^{{- j}\quad n}\frac{8}{P + {N\quad}_{n}^{r}}} \right. & (8)\end{matrix}$

[0090] In the following steps of the method, the two impulse responsescorresponding to the Probe n−1 and to the Probe n are estimated againand the operation is terminated by applying an equalization algorithm,for example the BDFE algorithm properly speaking.

[0091] Joint Estimation of the Two Impulse Responses

[0092] The assumption made here is that the impulse response of thechannel develops “linearly” between the two estimations.

[0093] It is considered here that the j^(th) (j−0. . . L−1) sample ofthe generalized impulse response (variable in time) passes from h_(j)^((n0)) at a sample with a position n₀, to h_(j) ^((n1)) at a samplewith a position n₁.

[0094] This progress is expressed by the following L differences:$\begin{matrix}{{dh}_{j}^{({n0})} = \frac{h_{j}^{({n1})} - h_{j}^{({n0})}}{n_{1} - n_{0}}} & (9)\end{matrix}$

[0095] The value of the sample r_(n) received at the position n is thengiven by: $\begin{matrix}{r_{n} = {\sum\limits_{j = 0}^{L - 1}{\left( {h_{j}^{({n0})} + {\frac{n - j - n_{0}}{n_{1} - n_{0}}\left( {h_{j}^{({n1})} - h_{j}^{({n0})}} \right)}} \right)e_{n - j}\quad {or}\quad {again}\text{:}}}} & (10) \\{r_{n} = {\frac{1}{n_{1} - n_{0}}{\sum\limits_{j = 0}^{L - 1}{\left( {{\left( {n_{1} - n + j} \right)h_{j}^{({n0})}} + {\left( {n - j - n_{0}} \right)h_{j}^{({n1})}}} \right)e_{n - j}}}}} & (11)\end{matrix}$

[0096] The symbols sent out for the probe Probe n−1 preceding the blockof data to be demodulated (the values a_(i)) and those for the probeProbe n following it (the values c_(i)) are known.

[0097] The joint estimation of the preceding impulse responses(pertaining to the position −P) and following impulse responses(pertaining to the position N) will consist in minimizing the followingerror (1): $\begin{matrix}{{\left( {N + P} \right)^{2}E} = {\sum\limits_{i = {L - 1 - P}}^{- 1}\left| {{\sum\limits_{j = 0}^{L - 1}{a_{i - j}\left( {{\left( {N - i + j} \right)h_{j}^{({- P})}} + {\left( {i - j + P} \right)h_{j}^{(N)}}} \right)}} -} \right.}} \\{{{\left( {N + P} \right)r_{i}}}^{2} +} \\{{\sum\limits_{i = {N + L - 1}}^{N + P - 1}\left| {\sum\limits_{j = 0}^{L - 1}{c_{i - j}\left( {{\left( {N - i + j} \right)h_{j}^{({- P})}} +} \right.}} \right.}} \\\left. {\left. {\left( {i - j + P} \right)h_{j}^{(N)}} \right) - {\left( {N + P} \right)r_{i}}} \right|^{2}\end{matrix}$

[0098] in this example, everything has been multiplied by (N+p)²

[0099] To clarify the problem, the following are laid down:$\begin{matrix}{{r_{m}^{NP} = {\left( {N + P} \right)r_{m + L - 1 - P}}}\quad} \\{{{si}\quad m} = {{0\quad \ldots \quad P} - L}} \\{r_{m}^{NP} = {\left( {N + P} \right)r_{m + N + {2L} - 2 - P}}} \\{{{si}\quad m} = {P - L + {1\quad \ldots \quad 2\quad P} - {2L} + 1}} \\{h_{k}^{NP} = h_{k}^{({- P})}} \\{{{si}\quad k} = {{0\quad \ldots \quad L} - 1}} \\{h_{k}^{NP} = h_{k - L}^{(N)}} \\{{{si}\quad k} = {{L\quad \ldots \quad 2\quad L} - 1}} \\{a_{m,k}^{NP} = {\left( {N + P - L + 1 - m + k} \right)a_{L - 1 - P + m - k}}} \\{{{{si}\quad m} = {{{0\quad \ldots \quad P} - {L\quad {et}\quad k}} = {{0\quad \ldots \quad L} - 1}}}{a_{m,k}^{NP} = {\left( {{2\left( {L - 1} \right)} + 1 + m - k} \right)a_{{2{({L - 1})}} - P + 1 + m - k}}}} \\{a_{m,k}^{NP} = {\left( {P - {2\left( {L - 1} \right)} - m + k} \right)c_{N + {2{({L - 1})}} - P + m - k}}} \\{{{si}\quad m} = {{P - L + {1\quad \ldots \quad 2P} - {2L} + {1\quad {et}\quad k}} = {{0\quad \ldots \quad L} - 1}}} \\{a_{m,k}^{NP} = {\left( {N + {3\left( {L - 1} \right)} + 1 + m - k} \right)c_{N + {3{({L - 1})}} - P + 1 + m - k}}} \\{{{si}\quad m} = {{P - L + {1\quad \ldots \quad 2\quad P} - {2L} + {1\quad {et}\quad k}} = {{L\quad \ldots \quad 2L} - 1}}}\end{matrix}$

[0100] We then have (13):${\left( {N + P} \right)^{2}E} = {\sum\limits_{m = 0}^{{2\quad P} - {2\quad L} + 1}{{{\sum\limits_{k = 0}^{{2\quad L} - 1}{a_{m,k}^{NP}h_{k}^{NP}}} - r_{m}^{NP}}}^{2}}$

[0101] The cancellation of the derivatives gives the following 2Lequations: $\begin{matrix}{{{\sum\limits_{k = 0}^{{2\quad L} - 1}{h_{k}^{NP}\left( {\sum\limits_{\underset{p = {{0\quad \ldots \quad 2L} - 1}}{m = 0}}^{{2\quad P} - {2L} + 1}{a_{m,k}^{NP}a_{m,p}^{{NP}^{*}}}} \right)}} = {\sum\limits_{m = 0}^{{2\quad P} - {2L} + 1}{r_{m}^{NP}a_{m,p}^{{NP}^{*}}}}}{{\sum\limits_{k = 0}^{{2\quad L} - 1}{A_{k,p}^{NP}h_{k}^{NP}}} = {\sum\limits_{\underset{p = {{0\quad \ldots \quad 2L} - 1}}{m = 0}}^{{2\quad P} - {2L} + 1}{r_{m}^{NP}a_{m,p}^{{NP}^{*}}\quad {with}}}}{A_{k,p}^{NP} = {\sum\limits_{\underset{\underset{p = {{0{\ldots 2}\quad L} - 1}}{k = {{0{\ldots 2}\quad L} - 1}}}{m = 0}}^{{2P} - {2L} + 1}{a_{m,k}^{NP}a_{m,p}^{{NP}^{*}}}}}} & (14)\end{matrix}$

[0102] This system of Hermitian equations is resolved, for example, byusing the methods commonly known to those skilled in the art, and givesthe values of the two impulse responses sought, h^((−P)) (L firstunknowns) and h^((N)) (L last unknowns), valid respectively at the startof the probe before the data and at the start of the probe after thedata.

[0103] In practice, the matrices L and U deduced from A_(NP) are onceagain pre-computed (for example in a read-only memory) since the matrixA^(NP) is formed out of constant values.

[0104] It can then be shown that the total mean square error (give ortake a constant multiplier factor) has the value: $\begin{matrix}\begin{matrix}{E_{\min} = {\sum\limits_{m = 0}^{{2\quad P} - {2L} + 1}\left| r_{m}^{NP} \middle| {}_{2}{- {\sum\limits_{k = 0}^{{2\quad L} - 1}A_{k,k}^{NP}}} \middle| h_{k}^{NP} \middle| {}_{2} - \right.}} \\{2\quad {{Re}\left( {\sum\limits_{k = 0}^{{2L} - 2}{h_{k}^{NP}{\sum\limits_{j = {k + 1}}^{{2L} - 1}{h_{j}^{{NP}^{*}}A_{k,j}^{NP}}}}} \right)}}\end{matrix} & (16)\end{matrix}$

[0105] The mean square error can be used to choose the sampling positionfor which it has the lowest value. This makes it possible to carry outan end-of-synchronization follow-up operation.

[0106] The next step of the method consists, for example, of theapplication of a BDFE algorithm with interpolation.

[0107] BDFE Algorithm with Interpolation

[0108] 1 The BDFE algorithm is used to find the most probable values forthe b1 values, namely symbols of unknown data. It being known that asample r_(n) is expressed as: $\begin{matrix}{r_{n} = {\frac{1}{P + N}{\sum\limits_{j = 0}^{L - 1}{\left( {{\left( {N - n + j} \right)h_{j}^{({- P})}} + {\left( {n - j + P} \right)h_{j}^{(N)}}} \right)e_{n - j}}}}} & (17)\end{matrix}$

[0109] the following notations are used for greater clarity:${dh}_{j} = \frac{\begin{matrix}{h_{j} = h_{j}^{({- P})}} \\{h_{j}^{(N)} - h_{j}^{({- P})}}\end{matrix}}{P + N}$

[0110] so much so that r_(n) can be rewritten: $\begin{matrix}{r_{n} = {\sum\limits_{j = 0}^{L - 1}{e_{n - j}\left( {h_{j} + {\left( {n - j + P} \right){dh}_{j}}} \right)}}} & (18)\end{matrix}$

[0111] In a first stage, the method eliminates the signal influenced bythe b_(i), values and the share due to the preceding probes (Probe n−1)and the following probes (Probe n).

[0112] The samples r_(n) are then replaced by the corrected values r_(n)^(c) defined by the following three expressions (19): $\begin{matrix}{r_{i}^{c}\quad = {~~}{r_{i}\quad - \quad {\sum\limits_{j\quad = \quad {i\quad + \quad 1}}^{L\quad - \quad 1}{{a\quad}_{i\quad - \quad j}\left( \quad {h_{j}\quad + \quad {\left( {i\quad - \quad j\quad + \quad P} \right)\quad {dh}_{j}}} \right)}}}} \\{i\quad = {~~}{{O\quad \ldots \quad L}\quad - \quad 2}} \\{r_{i}^{c}\quad = {~~}r_{i}} \\{i\quad = {~~}{L\quad - \quad {1\quad \ldots \quad N}\quad - \quad 1}} \\{r_{i}^{c}\quad = {~~}{r_{i}\quad - \quad {\sum\limits_{j\quad = \quad 0}^{i\quad - \quad N}{c_{i\quad - \quad j}\left( \quad {h_{j}\quad + \quad {\left( {1\quad - \quad j\quad + \quad P} \right)\quad {dh}_{j}}} \right)}}}} \\{i\quad = {~~}{{N\quad \ldots \quad N}\quad + \quad L\quad - \quad 1}}\end{matrix}$

[0113] The symbols received then no longer depend on any values otherthan the b₁ values, that is: $\begin{matrix}{{r_{i}^{c} = {\sum\limits_{j = {{MAX}{({{O,\quad i} - N + 1})}}}^{{MIN}{({{i,\quad L} - 1})}}\quad {b_{1 - j}\left( {h_{j} + {\left( {i - j + P} \right){dh}_{j}}} \right)}}}{i = {{O\quad \ldots \quad N} + L - 1}}} & (20)\end{matrix}$

[0114] Then, for further simplification, we write:

h _(j,i) =h _(j)+(i+P)dh _(j)

[0115] (j^(th) sample of the impulse response of the channel at thearrival of the symbol i, it being known that its value was h₀. . .h_(L−1) at the symbol−P)

[0116] We can then write: $\begin{matrix}{{r_{i}^{c} = {\sum\limits_{k = {{MAX}{({{0{,\quad}\quad i} - L + 1})}}}^{{MIN}{({N - {1,\quad i}})}}\quad {b_{k}h_{i - {k,\quad k}}}}}{i = {{O\quad \ldots \quad N} + L - 1}}} & (21)\end{matrix}$

[0117] This makes it possible simply to obtain the b₁ values inminimizing the quantity: $\begin{matrix}{E = {{\sum\limits_{i = 0}^{N + L - 1}{\quad \left| {{\sum\limits_{k = {{MAX}{\{{{0,\quad i} - L + 1})}}}^{{MIN}{({N - {1,\quad i}})}}\quad {b_{k}h_{i - {k,\quad k}}}} - r_{i}^{c}} \middle| {}_{2}m \right.}} = {{O\quad \ldots \quad N} - 1}}} & (22)\end{matrix}$

[0118] It is then necessary to resolve the following system of Nequations: $\begin{matrix}{{{\sum\limits_{i = 0}^{N + L - 1}{\quad {h_{i - {m,\quad m}}^{*}\left( {{\sum\limits_{k = {{MAX}{({{0,\quad i} - L + 1})}}}^{{{MIN}{({{N - 1}{,\quad i}})}}\quad}\quad {b_{k}h_{i - {k{,\quad}\quad k}}}} - r_{i}^{c}} \right)}}} = 0}{m = {{O\quad \ldots \quad N} - 1}}{{that}\quad {is}\text{:~~~~~~~~~~~~~~~~~~~~~~~~~~~}}\text{}\begin{matrix}{{\sum\limits_{k = {{MAX}{({{0,\quad m} - L + 1})}}}^{k = {{MIN}{({N - {1{,\quad}\quad m} + L - 1})}}}{b_{k}{\sum\limits_{i = {{MAX}{({k,\quad m})}}}^{i = {{MIN}{({k + L - {1{,\quad}\quad m} + L - 1})}}}\quad {h_{i - {k,\quad k}}h_{i - {m,\quad m}}^{*}}}}} = {\sum\limits_{i = m}^{L + m - 1}\quad {r_{i}^{c}h_{i - {m,\quad m}}^{*}}}}\end{matrix}{m = {{O\quad \ldots \quad N} - 1}}} & (23)\end{matrix}$

[0119] Coefficient of b_(k) in the equation m: $\begin{matrix}{B_{m,\quad k} = {\sum\limits_{i = {{MAX}{({k{\quad,}\quad m})}}}^{i = {{MIN}{({k + L - {1{,\quad}\quad m} + L - 1})}}}\quad {h_{{i - {k,\quad i}}\quad}h_{i - {m,\quad i}}^{*}}}} & (24)\end{matrix}$

[0120] The problem can be simplified by iteration, in considering onlythe upper part of the matrix B.

[0121] Indeed, the following relationship of recurrence is shown:$\begin{matrix}{{{B_{{k,\quad k} + p} = {B_{k - {1,\quad k} - 1 + p} + F_{p} + {\left( {{2k} - 1} \right)G_{{p\quad }\quad}}}}{G_{p} = {\sum\limits_{q = 0}^{q = {L - 1 - p}}\quad {{dh}_{q + p}^{*}{dh}_{q}\quad \text{(}{note}\text{:}G_{0}\quad r\quad {éel}\quad \text{)}}}}}\begin{matrix}{F_{p} = {{\left( {p + {2P}} \right)G_{p}} + {\sum\limits_{q = 0}^{q = {L - 1 - p}}{\quad {dh}_{q}h_{q + p}^{*}}} +}} \\{{{dh}_{q + p}^{*}h_{q}\quad \text{(}\text{note:}F_{0}\quad r\quad {éel}\text{)}}}\end{matrix}\quad \quad {p = {{O\quad \ldots \quad L} - 1}}} & (25)\end{matrix}$

[0122] To avoid problems of computation precision, it is preferable tocompute first of all the coefficients B_(0,0 L−1), then the followingones, by the relationship: $\begin{matrix}{\begin{matrix}{B_{0,\quad p} = {\sum\limits_{i = p}^{i = {L - 1}}\quad {\left( {h_{i - p} + {\left( {p + P} \right){dh}_{i - p}}} \right)\left( {h_{i}^{*} + {Pdh}_{i}^{*}} \right)}}} \\{= {\sum\limits_{q = 0}^{L - 1 - p}\quad {\left( {h_{q} + {\left( {p + P} \right){dh}_{q}}} \right)\left( {h_{p + q}^{*} + {Pdh}_{p + q}^{*}} \right)}}} \\{\left( {\text{note:~~}B_{0,\quad 0}\quad r\quad {éel}} \right)}\end{matrix}\quad {p = {{O\quad \ldots \quad L} - 1}}{B_{{k,\quad k} + p} = {B_{0,\quad p} + {kF}_{p} + {k^{2}G_{p}}}}{k = {{1\quad \ldots \quad N} - 1}}} & (26)\end{matrix}$

[0123] This makes it possible, once the first line of B has beencomputed, to compute the following lines by a one-line shift andone-column shift, and by simple modification.

[0124] To improve the computation precision, (notably in fixed-pointnotation) it is also possible to use the following (exact) formulae forp=0 . . . L−1: $\begin{matrix}{B_{0} = B_{0,\quad p}} \\{B_{1} = B_{\frac{N}{2},{\frac{N}{2} + p}}} \\{B_{2} = B_{{N,\quad N} + p}}\end{matrix}$

[0125] (in fact, B₂ normally does not exist since its indices are beyondlimits) These three quantities are all of the same magnitude. Thisprevents problems of readjustment when using processors working withfixed-point notation.

[0126] Then, for all the values of p, namely p=. . . L−1the followingoperation is done:

a _(p)0,=B ₀

a _(p,1)=−3B ₀+4B ₁ −B ₂

a _(p,2)=2(B ₀−2B ₁ +B ₂)

[0127] and finally, for m=0. . . N−1:$B_{{m,\quad m} + p} = {{a_{p,\quad 0} + {{x\left( {a_{p,\quad 1} + a_{p,\quad 2}} \right)}\quad {with}\quad x}} = \frac{m}{N}}$

[0128] It is noted that the quantity ×is a number ranging from 0 to 1,thus facilitating the computations.

[0129] The matrix B computed here has the form:$B = \left| \begin{matrix}B_{0,\quad 0} & B_{0{,\quad 1}} & ⋰ & B_{{0{,\quad}\quad L} - 1} & 0 & 0 & 0 \\B_{{0{,\quad 1}}\quad}^{*} & B_{1,\quad 1} & B_{{1,\quad 2}\quad} & ⋰ & B_{1,\quad L} & 0 & 0 \\⋰ & B_{1,\quad 2}^{*} & B_{2,\quad 2} & B_{2,\quad 3} & ⋰ & ⋰ & 0 \\B_{{0,\quad L} - 1}^{*} & ⋰ & B_{2,3}^{*} & B_{3{,\quad}3} & B_{3,\quad 4} & ⋰ & B_{N - {L{,\quad}\quad N} - 1} \\0 & B_{1,\quad L}^{*} & ⋰ & B_{3,\quad 4}^{*} & B_{4,\quad 4} & ⋰ & ⋰ \\0 & 0 & B_{{2,\quad L} + 1}^{*} & ⋰ & ⋰ & ⋰ & B_{N - {2,\quad N} - 1} \\0 & 0 & 0 & B_{N - {L,\quad N} - 1}^{*} & ⋰ & B_{N - {2,\quad N} - 1}^{*} & B_{N - {1,\quad N} - 1}\end{matrix} \right|$

[0130] The decomposition L−U will give two matrices L and U with theform: $U = {\begin{matrix}u_{0,0} & u_{0,1} & ⋰ & u_{0,{L - 1}} & 0 & 0 & 0 \\0 & u_{1,1} & u_{1,2} & ⋰ & u_{1,L} & 0 & 0 \\0 & 0 & u_{2,2} & u_{2,3} & ⋰ & ⋰ & 0 \\0 & 0 & 0 & u_{3,3} & u_{3,4} & ⋰ & u_{{N - L},{N - 1}} \\0 & 0 & 0 & 0 & u_{4,4} & ⋰ & ⋰ \\0 & 0 & 0 & 0 & 0 & ⋰ & u_{{N - 2},{N - 1}} \\0 & 0 & 0 & 0 & 0 & 0 & u_{{N - 1},{N - 1}}\end{matrix}}$ $L = {\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 \\1_{1,0} & 1 & 0 & 0 & 0 & 0 & 0 \\⋰ & 1_{2,1} & 1 & 0 & 0 & 0 & 0 \\1_{{L - 1},0} & ⋰ & 1_{3,2} & 1 & 0 & 0 & 0 \\0 & 1_{L,1} & ⋰ & 1_{4,3} & 1 & 0 & 0 \\0 & 0 & 1_{{L + 1},2} & ⋰ & ⋰ & ⋰ & 0 \\0 & 0 & 0 & 1_{{N - 1},{N - L}} & ⋰ & 1_{{N - 1},{N - 2}} & 1\end{matrix}}$

[0131] Since

[0132] the matrix B, although it is large-sized, contains only fewnon-zero elements the matrix B is Hermitian (it is therefore unnecessaryto compute its lower triangle for example)

[0133] once the matrices L and U are computed, the matrix B is no longerused

[0134] the computations can be organized in such a way that the elementsof L and U gradually replace the elements of B in the same memory zone,B is stored in a unique matrix having dimensions N×(2L−1) as follows(the left-hand part of the central column is not computed):$B = {\begin{matrix}0 & 0 & 0 & B_{0,0} & B_{0,1} & \cdots & B_{0,{L - 1}} \\0 & 0 & \left( B_{0,1}^{*} \right) & B_{1,1} & B_{1,2} & \cdots & B_{1,L} \\0 & \ddots & \left( B_{1,2}^{*} \right) & B_{2,2} & \cdots & B_{2,3} & \vdots \\\left( B_{0,{L - 1}}^{*} \right) & \cdots & \left( B_{2,3}^{*} \right) & B_{3,3} & B_{3,4} & \cdots & B_{{N - {L.}},{N - 1}} \\\left( B_{1,L}^{*} \right) & \cdots & \left( B_{3,4}^{*} \right) & B_{4,4} & \cdots & \ddots & 0 \\\vdots & \cdots & \cdots & \vdots & B_{{N - 2},{N - 1}} & 0 & 0 \\\left( B_{{N - L},{N - 1}}^{*} \right) & \cdots & \left( B_{{N - 2},{N - 1}}^{*} \right) & B_{{N - 1},{N - 1}} & 0 & 0 & 0\end{matrix}}$

[0135] During the decomposition L−U, the same memory zone is used andits contents, at the end of the decomposition, is the following (itmaybe recalled that the diagonal of L contains only ones and thereforedoes not need to be stored): ${LU} = {\begin{matrix}0 & 0 & 0 & U_{0,0} & U_{0,1} & \cdots & U_{0,{L - 1}} \\0 & 0 & L_{0,1} & U_{1,1} & U_{1,2} & \cdots & U_{1,L} \\0 & \ddots & L_{1,2} & U_{2,2} & \cdots & U_{2,3} & \vdots \\L_{0,{L - 1}} & \cdots & L_{2,3} & U_{3,3} & U_{3,4} & \cdots & U_{{N - L},{N - 1}} \\L_{1,L} & \cdots & L_{3,4} & U_{4,4} & \quad & \ddots & 0 \\\vdots & \cdots & \cdots & \vdots & U_{{N - 2},{N - 1}} & 0 & 0 \\L_{{N - L},{N - 1}} & \cdots & L_{{N - 2},{N - 1}} & U_{{N - 1},{N - 1}} & 0 & 0 & 0\end{matrix}}$

[0136]FIG. 4 gives a schematic view of the structure of a deviceaccording to the invention. The signal or signals are preconditionedafter passage into a set of commonly used devices comprising adaptedfilters, an AGC (automatic gain control device, etc.) and all thedevices enabling the preconditioning, and this signal or signals is orare transmitted for example to a microprocessor 1 provided with asoftware program designed to execute

What is claimed is: 1- A method for the equalization of the signalreceived by a receiver, said signal comprising at least one known datasequence (or probe) and a data block located between a first probe Proben−1 and a second probe Probe n comprising at least one step for theestimation of the phase rotation θ of the signal received between thestart of the data block and the end of the data block. 2- A methodaccording to claim 1 wherein it estimates the phase rotation between thefirst Probe n−1 positioned before the data block to be demodulated andthe second probe Probe n positioned after the data block to bedemodulated. 3- A method according to one of the claims 1 and 2comprising a step in which the impulse response of the channel isestimated, firstly, by using the first Probe n−1 and, secondly, by usingthe second Probe n and a step in which the difference between these twoestimated impulse response values is minimized. 4- A method according toclaim 3, wherein the difference between the estimated values of theimpulse response of the channel can be expressed for example in theform:$E = {\sum\limits_{i = 0}^{L - 1}\left| {h_{i}^{(N)} - {^{j\theta}h_{i}^{({- P})}}} \right|^{2}}$

and wherein the optimum value of the phase rotation θ is determined asbeing the argument of the sum of the conjugate products, that is:$\theta = {\arg\left( {\sum\limits_{i = 0}^{L - 1}{h_{i}^{(N)}h_{i}^{{({- P})}*}}} \right)}$

5- A method according to one of the claims 1 and 2 comprising at leastthe following steps: a) estimating the impulse responses h₀(t) and h₁(t)of the probes positioned on either side of the block of data to beanalyzed, b) estimating the rotation of the phase, θ, c) correcting thephase of the frequency of the signal received, and performing a reverserotation on the data block and the probes, d) again jointly estimatingthe impulse responses by means of the modified probes, e) applying aBDFE type data block equalization algorithm with feedback loop. 6- A useof a method according to one of the claims 1 to 5 to the demodulation ofsignals received in a BDFE. 7- A device for equalizing at least onesignal that has traveled through a transmission channel, said signalcomprising at least one data block and several probes located on eitherside of the data block, wherein the device comprises at least one meansreceiving the signals and adapted to determining the phase rotation 0 ofthe signal or signals received, between a first Probe (n−1) locatedbefore the data block and a second Probe (n) positioned after the datablock, correcting the phase of the received signal, estimating theresponses by means of the probes thus modified and applying a BDFE typealgorithm.